Research On Decoupling Method Of Stokes-Darcy Model Based On Spectral Deferred Correction

Multi-domain and multi-physical phenomenon is very common in engineering applications.Therefore,the modeling and calculation of coupling complex fluid has always been a hot topic in the field of computational mathematics.As a typical coupling model,Stokes-Darcy coupling system is widely used in simulating surface water-groundwater system,oil exploitation,blood flow in blood vessels and so on.Considering the evolutionary Stokes-Darcy coupling model with Beavers-Joseph-Saffman interface conditions,based on the first-order decoupling algorithm,we propose a new secondorder decoupling algorithm adopting the idea of spectral deferred correction.Theoretically,we analyze the stability and error estimation of our proposed semi-implicit spectral deferred correction second-order decoupling algorithm.Numerically,we compare the CPU time of the first-order coupling algorithm,the first-order decoupling algorithm and the semi-implicit secondorder spectral deferred correction decoupling algorithm,and under the same space scale and time step scale,we compare the convergence accuracy of the first-order decoupling algorithm and our proposed second-order decoupling algorithm,it is easy to see that two decoupling algorithms are more efficient than that of the coupling algorithm,which is consistent with the fact that decoupling the system can reduce the scale of the coupling model,moreover,the numerical results indicate that the convergence accuracy of our proposed algorithm is better than the first-order decoupling algorithm;Secondly,our spectral deferred corrected decoupling algorithm can achieve the optimal second-order convergence when the time step is properly selected;We compare the proposed algorithm with the spectral deferred correction second-order coupling algorithm,the computational efficiency of the proposed algorithm is significantly higher than that of the coupling algorithm;Finally,we display the numerical results of our second-order spectral deferred correction decoupling algorithm with other existing of three second-order decoupling algorithms based on high-order time discrete format,as well as the algorithm based on time filter technique,the numerical results of our proposed algorithm are comparable to the other four algorithms,and the proposed algorithm is easy to implement.All in all,the second-order decoupling algorithm based on spectral deferred correction technique proposed in this paper provides a new idea of constructing high-order algorithm,and the theoretical analysis also lays a foundation for extending this idea to other models.